The multi-terminal vertex separator problem: Branch-and-Cut-and-Price

We are given a graph G=(V?T,E), with V?T the set of vertices where T is terminals and E edges. The multi-terminal vertex separator problem consists in finding subset S?V minimum size intersecting all paths between every pair terminals. In this paper we present three extended linear integer programming formulations for develop Branch-and-Price Branch-and-Cut-and-Price algorithms. For each formulation pricing problem, branching scheme computation dual bound used during column generation phase. Computational results reported comparing performance on instances.